Hi Christoph, I'm glad you liked the tutorial, thanks for your kind words!
Actually it is really easy to upgrade to Bootstrap 3.1.1, you don't need to change default.ascx at all.
In fact all you have to do is download Bootstrap 3.1.1 by clicking the Download Bootstrap button on this page: http://getbootstrap.com/getting-started/
Unzip the package and copy everything from of the css folder into your skin CSS folder. (Overwrite the files that are already there).
Copy everything from the Bootstrap JS folder into your skin JS folder (Overwriting again).
If you are working on a local copy of DNN then you have successfully upgraded, if you are working remotely, upload those two altered folders and you're done.